Journal of Inequalities and Applications - Latest Articles

Refinements of Hermite-Hadamard's type inequalities for operator convex functions

Vildan Bacak — 2013-05-24T00:00:00Z

The purpose of this paper is to present some new versions of Hermite-Hadamards type inequalities for operator convex functions. We give refinements of Hermite-Hadamards type inequalities for convex functions of selfadjoint operators in Hilbert space analogous to well known inequalities the same type.The results presented in this paper are more general than known results given by several authors.

Asymptotic properties of wavelet-based estimator in nonparametric regression model with weakly dependent processes

Xing-cai Zhou — 2013-05-23T00:00:00Z

In this paper, we consider a nonparametric regression model with replicated observations based on the varphi-mixing and the rho-mixing error's structures respectively, for exhibiting dependence among the units. The wavelet procedures are developed to estimate the regression function. Under suitable conditions, we obtain expansions for the bias and the variance of wavelet estimator, prove the moment consistency, the strong consistency, the strong convergence rate of its, and establish the asymptotic normality of wavelet estimator.

Convergence of Halley's method for operators with the bounded second derivative in Banach spaces

I.K. Argyros — 2013-05-23T00:00:00Z

In this paper, we present a semi-local convergence analysis of Halley's method for approximating a locally unique solution of a nonlinear equation in a Banach space setting, where we assume that the second Fr\'{e}chet-derivative is bounded. Numerical examples are used to show that the new convergence criteria can provide betterinformation than in earlier convergence criteria such as [1-7].

Bilinear Multipliers of Weighted Lebesgue Spaces and Variable Exponent Lebesgue Spaces

Öznur Kulak — 2013-05-23T00:00:00Z

Let 1[less than or equal to]p1,p2}dxidetais a bounded bilinear operator from L_{omega1}^{p1}(Rn)xL_{omega2}^{p2}(Rn) to L_{omega3}^{p3}(Rn). We denote by BM(p1,omega1;p2,omega2;p3,omega3) (shortly BM(omega1,omega2,omega3)) the vector space of bilinear multipliers of type (omega1,omega2,omega3).In this paper first we discuss some properties of the space BM(omega1,omega2,omega3). Furthermore, we give some examples of bilinear multipliers.At the end of this paper by using variable exponent Lebesgue spaces L^{p1(x)}(Rn), L^{p2(x)}(Rn) and L^{p3(x)}(Rn), we define the space of bilinear multipliers from L^{p1(x)}(Rn)xL^{p2(x)}(Rn) to L^{p3(x)}(Rn) and discuss some properties of this space.

Torricellian points in normed linear spaces

Sever Dragomir — 2013-05-22T00:00:00Z

Given a set of n (distinct) points A in a normed space, we consider the set of Torricellian points, that is, the set of points which minimises the sum of distances to the points in A. We introduce the Torricellian functional associated to a set of distinct points A, which calculates the sum of distances of a point x to the points in A. The Torricellian point is defined as the infimum (over all vectors) of this functional. We discuss the existence of Torricellian points in reflexive normed spaces, non-expansive subspaces and evidently, inner product spaces. A case for collinear points is given and is utilised to characterise strict convexity. For non-collinear case, it is shown that the set of Torricellian points contains a unique point when the space is strictly convex. However, we show that the uniqueness of Torricellian point of a non-collinear set does not characterise strictly convex. We consider a particular example of the Torricellian problem in a space endowed with the Taxicab geometry.

Boundedness of Faber Operators

YUNUS YILDIRIR — 2013-05-21T00:00:00Z

In this work, we prove the boundedness of the Faber operators that transform theHardy Orlicz class HM(D) into the Smirnov Orlicz class EM(G):

On Generalized Difference Lacunary Statistical Convergence in a Paranormed Space

Selma Altundag — 2013-05-20T00:00:00Z

In this article, we introduce the concept of Deltam- lacunary statisticalconvergence and Deltam- lacunary strongly convergence in a paranormedspace. Also, we establish some connections between these concepts.

Some results on Rockafellar-type iterative algorithms for zeros of accretive operators

Jong Soo Jung — 2013-05-20T00:00:00Z

We provide a new proof technique to obtain strong convergence of the sequences generated by viscosity iterative methods for Rockafellar type iterative algorithm and Halpern type iterative algorithm to a zero of accretive operator in Banach spaces. By using a new methoddifferent from previous ones, the main results improve and develop the recent well-known results in this area.

On some new matrix transformations

Rahmet Savas — 2013-05-20T00:00:00Z

In this paper, we characterize some matrix classes $(\omega(p,s), V_{\sigma }^{\lambda })$, $(\omega_p(s),V_{\sigma }^{\lambda })$ and $(\omega_p(s),V_{\sigma }^{\lambda })_{reg}$, under appropriate conditions

Some Unique Fixed Point Theorems For Rational Contractions In Partially Ordered Metric Spaces

Arshad Muhammad — 2013-05-17T00:00:00Z

In this paper, we prove some unique fixed point results for an perator T satisfying certain rational contraction condition in a partially ordered metric space. Our results generalize the main result of Jaggi [D.S. Jaggi, Some unique fixed point theorems, Indian J. Pure Appl. Maths, 8(2), (1977), 223-230]. We give several examples to show that our results are proper generalization of the existing one.